(1/37*x)+(1/22*x)=3

Solution for (1/37*x)+(1/22*x)=3 equation:

(1/37x)+(1/22x)=3

We move all terms to the left:

(1/37x)+(1/22x)-(3)=0


Domain of the equation: 37x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 22x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/37x)+(+1/22x)-3=0

We get rid of parentheses

1/37x+1/22x-3=0

We calculate fractions


22x/814x^2+37x/814x^2-3=0

We multiply all the terms by the denominator


22x+37x-3*814x^2=0

We add all the numbers together, and all the variables

59x-3*814x^2=0

Wy multiply elements

-2442x^2+59x=0

a = -2442; b = 59; c = 0;
Δ = b2-4ac
Δ = 592-4·(-2442)·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-59}{2*-2442}=\frac{-118}{-4884}
=59/2442
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+59}{2*-2442}=\frac{0}{-4884}
=0
$